UNC does not have a school of engineering. They offer biomedical engineering but it is not part of a traditional school of engineering. Chapel Hill and Carborro are amazing college towns and absolutely do not feel like a large city. They feel like traditional college towns. As far as parties, you will find them off campus if you want them. If you have no interest, you can choose never to see them. There are plenty of things to do on and off campus at CH that do not involve parties. Michigan is the larger school; UNC has about 18,000 undergrads versus Michigan’s 28,000. Michigan also has more graduate students - approximately 15,000 versus 10,000 at UNC.
You will get top notch math and science opportunities at both schools, but if you are looking for a traditional school of engineering I would attend Michigan. If you are interested in biomedical engineering, the program at UNC will land you excellent internships and the students I know who graduated from the program received job offers immediately.
I can’t answer the question about FA.